The present invention relates to methods and apparatus for management and control of annuities and distribution of annuity payments.
Annuities are contracts issued by insurers that provide one or more payments during the life of one or more individuals (annuitants). The payments may be contingent upon one or more annuitants being alive (a life-contingent annuity) or may be non-life-contingent. The payments may be made for a fixed term of years during a relevant life (an m-year temporary life annuity), or for so long as an individual lives (whole life annuity). The payments may commence immediately upon purchase of the annuity product or payments may be deferred. Further, payments may become due at the beginning of payment intervals (annuities-due), or at the end of payment intervals (annuities immediate). Annuities that provide scheduled payments are known as xe2x80x9cpayout annuities.xe2x80x9d Those that accumulate deposited funds (e.g, through interest credits or investment returns) are known as xe2x80x9caccumulation annuities.xe2x80x9d
Annuities play a significant role in a variety of contexts, including life insurance, disability insurance, and pensions. For example, life insurances may be purchased by a life annuity of premiums instead of a single premium. Also, the proceeds of a life insurance policy payable upon the death of the insured may be converted through a settlement option into an annuity for the beneficiary. An annuity may be used to provide periodic payments to a disabled worker for so long as the worker is disabled. Retirement plan contributions may be used to purchase immediate or deferred annuities payable during retirement.
A life annuity may be considered as a guarantee that its owner will not outlive his or her payout, which is a guarantee not made by non-annuity products such as mutual funds and certificates of deposit (CDs). (Note that the terms xe2x80x9cowner,xe2x80x9d xe2x80x9cannuitant,xe2x80x9d xe2x80x9cannuity purchaser,xe2x80x9d or xe2x80x9cinvestorxe2x80x9d need not refer to the same person. Herein, the terms will be used interchangeably with the meaning being understood by context.) Payout annuities can provide fixed, variable, or a combination of fixed and variable annuity payments. A fixed annuity guarantees certain payments in amounts determined at the time of contract issuance. A variable annuity will provide payments that vary with the investment performance of the assets that underlie the annuity contract. These assets are typically segregated in a separate account of the insurer. A combination annuity pays amounts that are partly fixed and partly variable.
Both fixed and variable annuities can guarantee scheduled payments for life or for a term of years. A fixed annuity offers the security of guaranteed, pre-defined periodic payments. A variable annuity also guarantees periodic payments, but the amount of each payment will vary with investment performance. Favorable investment performance will generate higher payments. This is a major benefit during inflationary periods because the growth in payments may offset the devaluation of money caused by inflation. In contrast, fixed annuities provide fixed payments that become successively less valuable over time in the presence of inflation.
Although investment returns are not guaranteed to the owner of a variable annuity, the owner has the opportunity to achieve investment results that provide ultimately higher payments than provided by the fixed annuity payment. The range of investment options associated with variable annuity contracts is quite broad, ranging from fixed income to equity investments. Typically, the consideration paid for the variable annuity fund will be used to purchase the underlying assets. The annuitant is then credited with the performance of the assets.
At all times, the insurer must maintain adequate financial reserves to make future annuity benefit payments. The reserves of an annuity fund and the benefits payable will be affected by a plurality of factors such as mortality rates, assumed investment return, investment results and administrative costs. Actuarial mortality tables may be used to determine the expected future lifetime of an individual and aggregates of individuals. The future lifetime may be thought of as a random variable that affects the distribution of payments over time for a single annuity or aggregates of annuities. Typically, mortality assumptions will be made at the time of contract issuance based upon actuarial mortality tables. Mortality tables may reflect differences in actuarial data for males and females, and may comprise different data for individual markets and group markets. The insurer bears the risk that the annuitant will live longer than predicted. The annuitant bears the risk of dying sooner than expected. The future performance of the underlying investments may also be estimated by assuming an expected rate of return on the investments. The investment performance will affect the available reserves in any given payment interval and will also affect the present value of a benefit payment to be made in a given payment interval. The present value of a single payment to be made in the future may be thought of as a random variable:
yt=btvt
where yt is the present value of the benefit payment, bt, and vt is the interest discount factor from the time of payment back to the present time. Thus, vt is itself a random variable dependent upon market factors.
The present value of an annuity is therefore a random function, Y, of random variables representing interest and the future lifetime of the annuitant. The actuarial present value, xc3xa4x, of an annuity for a life at age x 10 is the expected value of Y, E[Y]. For example, for a whole-life annuity-due that pays a unit amount at each payment period, k, the actuarial present value of the annuity may be expressed as:                                           a            ¨                    x                =                              ∑                          k              =              0                        ∞                    ⁢                      xe2x80x83                    ⁢                                    v              k              k                        ⁢                          p              k                                                          (        1        )            
where: vk is the interest discount factor for a payment at the kth payment interval and kpx is the probability that a life at age x survives to age x+k, as determined from actuarial mortality tables. To simplify analysis, it is commonly assumed by actuaries that the effective interest rate, i, is constant, so that the discount factor v is a constant given by v=(1+i)xe2x88x921.
Equation (1) defines a backward recursion relation for determining the actuarial present value of the annuity at any interval k, as follows:                                                                                                               a                    ¨                                    x                                =                                  xe2x80x83                                ⁢                                  1                  +                                                            ∑                                              k                        =                        0                                            ∞                                        ⁢                                          xe2x80x83                                        ⁢                                                                  v                                                  k                          +                          1                                                                          k                          +                          1                                                                    ⁢                                              p                        x                                                                                                                                                                    =                                  xe2x80x83                                ⁢                                  1                  +                                                            vp                      x                                        ⁢                                                                  ∑                                                  k                          =                          0                                                ∞                                            ⁢                                              xe2x80x83                                            ⁢                                                                        v                          k                          k                                                ⁢                                                  p                                                      x                            +                            1                                                                                                                                                                                                                      =                                  xe2x80x83                                ⁢                                  1                  +                                                            vp                      x                                        ⁢                                                                  a                        ¨                                                                    x                        +                        1                                                              ⁢                                          xe2x80x83                                        ⁢                    so                    ⁢                                          xe2x80x83                                        ⁢                    that                                                                                                                                                                a                    ¨                                                        x                    +                    k                                                  =                                  xe2x80x83                                ⁢                                  1                  +                                                            vp                                              x                        +                        k                                                              ⁢                                                                  a                        ¨                                                                    x                        +                        k                        +                        1                                                                                                                                ⁢                  xe2x80x83                                    (        2        )            
Similarly, recursion relations can be developed for other types of annuity structures.
The growth of the annuity funds will depend on the payments, bk, made at each interval, the investment returns on the funds, the premiums paid into the fund by the purchaser, and any expenses charged against the fund. Expenses incurred by the insurer will include taxes, licenses, and expenses for selling policies and providing services responsive to customer needs.
A typical annuity contract incorporates fixed assumptions concerning mortality and expenses at the time of contract inception. Positive or adverse deviations from these assumed distributions will be absorbed by the insurer. For a fixed annuity, the insurer bears the risk that the investment return guaranteed to the contract holder will be greater than the actual market performance attainable by investment of the fixed premium or premiums received from the payee.
In contrast, for a variable annuity, the risk that the investment return on assets underlying the annuity will exceed or fall below an investment return rate assumed at the time of contract issuance is passed to the contract holder.
This is done by computing a subsequent payment, bk+1, due at time k+1, from a prior payment, bk, at time k according to:                               b                      k            +            1                          =                              b            k                    ⁢                      xe2x80x83                    ⁢                                    1              +                              r                                  k                  +                  1                                                                    1              +              i                                                          (        3        )            
where:
rk+1 is the actual investment return in the interval from k to k+1; and
i is the assumed investment return (AIR).
(See, e.g., xe2x80x9cActuarial Mathematics,xe2x80x9d 2nd Ed., Bowers, et al., 1997, chapter 17.)
Clearly, if the assumed investment return (AIR) is smaller than the actual return (less expenses), the benefit level of a variable annuity will increase. Conversely, if the actual return (less expenses), falls below the AIR, the benefit level will decrease. Thus, the investment risk is borne by the annuity investor. Since variable annuity investors generally prefer that benefits increase rather than decrease over time, insurers will choose an AIR that is lower than the expected value of the actual investment return. For example, in recent markets the AIR has been in the range of about 4 to 6%.
The net consideration, xcfx80NET, for a paid-up annuity divided by the actuarial present value of the annuity for a life at age x establishes the initial value for the recursion relation of equation (3):
bo=xcfx80NET/xc3xa4xxe2x80x83xe2x80x83(4)
For a fixed annuity, all payments are equal so that:
bk+1=bk=bo=xcfx80Net/xc3xa4xxe2x80x83xe2x80x83(5)
However, the actuarial present value of the variable annuity is typically larger than the actuarial present value of the fixed annuity. This is because the AIR for a variable annuity tends to be lower than the return that may be assumed for a fixed annuity. A lower AIR results in a higher actuarial present value which in turn results in a lower initial benefit. Therefore, for the same net consideration, the initial payment of the variable annuity will be lower than the fixed payment provided by the fixed annuity. However, a lower AIR will result in future payments that increase faster or decline slower than would result from a higher AIR.
In order to achieve the same initial payment for both fixed and variable annuities, given the same net consideration, while ensuring adequate reserves, the actuarial present value of the variable annuity could be decreased by increasing the assumed investment return. But this would decrease the rate of growth of future payments to the annuity investor, thereby detracting from the marketability of the variable annuity. Thus, although present variable annuity systems have the desirable feature that payments will ultimately rise above the fixed level provided by the fixed annuity system, they possess the undesirable feature of lower initial payment levels.
Another disadvantage of presently available annuity systems is the inability to effectuate investor-preferred transfers from fixed to variable systems without incurring an undesirable future payment distribution. Using the paid-up annuity as an example, the net consideration allocable to the variable system at the time of transfer, kxe2x89xa70, from a fixed system will depend on the market value of the fixed annuity at time k:
xcfx80NET(k)=xc3xa4x+kFb0Fxe2x80x83xe2x80x83(6)
where the superscript, F, denotes values for the fixed annuity and b0 is the level fixed annuity payment. Upon transfer, the. payment at time k+1 will be:                               b                      k            +            1                          =                                                                              a                  ¨                                                  x                  +                  k                                F                            ⁢                              b                0                F                                                                    a                ¨                                            x                +                k                            V                                ·                                    1              +                              r                                  k                  +                  1                                                                    1              +              i                                                          (        7        )            
where the superscript, V, denotes values for the variable annuity.
Assuming once again an investment return for the variable annuity low enough to ensure that payments will increase over time and assuming a higher investment rate for the fixed annuity to ensure a valuation of the fixed annuity that is fair to the investor, then xc3xa4x+kF less than xc3xa4x+kV. Therefore, the discontinuity factor Rxe2x80x2=xc3xa4x+kF/xc3xa4x+kV will be less than 1, and the investor""s desired payment will be reduced by the factor Rxe2x80x2, and all subsequent future payments will be reduced. Comparable adverse consequences can easily be demonstrated for a transfer from a variable system to a fixed system.
Therefore, a need exists for a variable annuity system that provides initial payments as high as the fixed payment provided by the fixed annuity, while allowing transfer from a fixed annuity to the variable annuity and vice versa without incurring an undesirable future payment distribution resulting from the transfer.
Objects of the present invention are therefore to provide systems and methods for management and control of annuities and distribution of annuity payments that allow for transfers from fixed to variable annuities and vice versa without incurring undesirable future payment distributions. A further object of the present invention is to provide a variable annuity option with an initial payment as high as the payment provided by a fixed annuity for the same net consideration.
The present invention comprises an annuity system that allows transfers to or from a fixed annuity without discontinuity in the payment distribution to the annuitant. The invention also further allows for the initial payment of the variable annuity to be the same as the fixed annuity payments. This is accomplished by setting the initial payment of the variable annuity at the time of transfer or purchase equal to the fixed annuity payment and deriving the subsequent payments based on market interest rates at the time each payment is made. Each subsequent payment is based on a current pricing interest rate rather than a fixed assumed investment rate (AIR). The pricing interest rate may vary at each payment interval and may be tied to an objective market interest rate or indicator such as a treasury rate, a corporate bond rate, or other objective rate.
Compensation for the change in actuarial present value of the annuity as a result of a change in interest rates between payments is provided by an interest adjustment factor in the payment progression function. Thus, the annuitant receives full valuation of the transferor annuity without incurring an unfavorable future payment distribution from the transferee annuity.
A key advantage of the annuity system of the present invention is the enhanced flexibility offered to the contract owner. Permitting transfers out of the fixed fund allows the owner to change an otherwise irrevocable decision associated with fixed annuities. Funds allocated to the fixed fund can easily be transferred to a variable annuity investment fund at market value. To do this, future fixed annuity payments are discounted at current pricing interest rates and the amount of the transfer is transferred to an investment division corresponding to the assets underlying the variable fund.
The present invention may be implemented to provide payments that are part fixed and part variable. The investor may transfer some or all of his or her annuity funds from fixed annuities to variable annuities, from variable annuities to fixed annuities or from variable annuities to variable annuities. Payments from the transferor fund are reduced in proportion to the amount transferred, whereas the payments from the transferee fund are increased in proportion to the amount transferred.
The new method offers several key benefits to the annuity owner. These include: (1) the ability to move funds between fixed and variable annuities; (2) variable payments that start at the same level as fixed annuity contracts; (3) no undesirable payment distribution is incurred upon transfer to other investment choices; and (4) there is potentially less volatility in future payments.